If the penny doubles every year, then on the 1st birthday, the penny will become 2 pennies, on the 2nd birthday it will become 4 pennies, on the 3rd birthday it will become 8 pennies, and so on.
Therefore, on the 10th birthday, the penny will have doubled 9 times (since it doubles on each birthday except the first), so the total amount of money you will have is: 512 pennies on your 10th Birthday